I have come across the statement that propagation of singularities is a general feature of the hyperbolic equations (context: Einstein Field Equations). Even on an intuitive level, I cannot make sense out of it. To me it seems, that then any initial data we take will already contain the (Big Bang-) singularity, and therefore there is no such thing as a regular initial data.

Since Einstein Equations are hyperbolic, it means then that they will always (?!?) propagate the initial singularity? I would be grateful if anyone could explain how, in the context of general relativity, to understand the statement about the singularity propagation correctly. Thanks!

Please give a reference for the statement and quote it exactly. Otherwise we have no way to know what you're asking about. This was also posted on physics.SE: physics.stackexchange.com/questions/61676/… Please don't cross-post like this without telling people. It means that you're making people waste effort.
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Ben CrowellApr 20 '13 at 16:21

@BenCrowell here is the link cims.nyu.edu/~corona/hw/nlgonotes.pdf In the whole set of notes the context of initial singularity is not considered, that's what made me wonder. P.S: I deleted the physics.stackexchange post, sorry for the duplicate
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ConciseAndClearApr 20 '13 at 16:38

1 Answer
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You're right that singularities generically persist in hyperbolic PDEs. However, we typically don't actually include the instant of the Big Bang in our calculation, since nobody seriously believes GR is the correct theory to use in this regime (we need a full quantum theory at least) so we don't worry about this point.

Instead, we imagine starting a little bit after the initial 'moment', where everything is e.g. a nice smooth FLRW spacetime. You can then follow this back to a singularity, but you don't reach it before your theory breaks down.